Displaying child pages in sidebar

I would like to display in a PHP sidebar (using the PHP Code widget) the children of the currently displayed code. I’ve tried examples from the codex
http://codex.wordpress.org/Template_Tags/wp_list_pages
but what they consistently do is display children of the home page rather than those of the current page.

For instance

<?php
  if($post->post_parent)
  $children = wp_list_pages("title_li=&child_of=".$post->post_parent."&echo=0&depth=1");
  else
  $children = wp_list_pages("title_li=&child_of=".$post->ID."&echo=0&depth=1");
  if ($children) { ?>
  <ul>
  <?php echo $children; ?>
  </ul>
  <?php } ?>

(My only change was to add depth=1 since I don’t want the entire “web-map”, just the proper children of this page.)

Any thoughts?